>It's really the same method in different notation. You take the cross product and separate into parallel and perpendicular components, and then you reach the epsilon^2 equation, and it's the same from there.
Bivectors and cross-product aren't just different notation for the same thing if that's what you meant. They're distinct (but very much so related) mathematical structures. For one thing, one's associative while cross products break associativity.
As far as GA sharing a lot with the more comment vector algebra/calc methods. Personally, I'm happy that GA has an attitude of "if it's not broke, don't fix it". It also means there's really not a lot of time lost in the transition due to the compatibility. Hell it's even backwards compatible in the sense that you can still easily retrieve your axial vectors the cross product gave you if you so wish (which cleared up instantly what the exterior algebra folks were doing with their hodge star business when I decided I wanted to explore that perspective later on).
Bivectors and cross-product aren't just different notation for the same thing if that's what you meant. They're distinct (but very much so related) mathematical structures. For one thing, one's associative while cross products break associativity.
As far as GA sharing a lot with the more comment vector algebra/calc methods. Personally, I'm happy that GA has an attitude of "if it's not broke, don't fix it". It also means there's really not a lot of time lost in the transition due to the compatibility. Hell it's even backwards compatible in the sense that you can still easily retrieve your axial vectors the cross product gave you if you so wish (which cleared up instantly what the exterior algebra folks were doing with their hodge star business when I decided I wanted to explore that perspective later on).